We conducted classical molecular dynamics (MD) simulations to evaluate the mechanical properties and thermal conductivity of graphene springs, using the large scale atomic/molecular massively parallel simulatior package [1]}. To this aim, we used the optimized Tersoff potential parameter set proposed by Lindsay and Broido [2]} for introducing the atomic interaction between carbon. This version of Tersoff potential is not only highly computationally efficient, but also can yield accurate results for the mechanical and thermal properties of graphene. We analysed the mechanical response by conducting the uniaxial tensile simulations at room temperatures. For the evaluation of mechanical properties, we modified the cutoff of Tersoff potential from 0.18 nm to 0.20 nm to remove an unphysical stress pattern and moreover accurately reproduce the experimental results for the tensile strength of pristine graphene [3]}. In this case, the time increment of MD simulations was set at 0.25 fs. Before applying the loading conditions, all structures were equilibrated using Nosé-Hoover thermostat method. For the loading condition, a constant engineering strain rate of 1\(\times \) 10\(^8\)  s\(^{-1}\)  was applied, by increasing the periodic size of the simulation box along the loading direction in every time step. Virial stresses at every step were recorded and averaged over every 20 ps intervals to report the stress-strain relations.
To evaluate the thermal conductivity, we used equilibrium molecular dynamics (EMD) method. The time increment of EMD simulations was set at 0.25 fs. In the EMD method, the heat flux vector was calculated via:
\(\mathbf {J}(t) = \sum _i \left( e_i \mathbf {v}_i + \frac{1}{2} \sum _{i < j} \left(\mathbf {f}_{ij} \cdot \left(\mathbf {v}_i + \mathbf {v}_j\right)\right)\mathbf {r}_{ij}\right)\) 
